Finite Group Databasebeta

← #29575124

Subgroups — #29575124

Order 15616.

676 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454867C211yesmaximal, characteristic, complemented
2#21445763C211yesmaximal, characteristic, complemented
3#21445731C211yesmaximal, characteristic, complemented
4#21444310C211yesmaximal, characteristic, complemented
5#21443707C211yesmaximal, characteristic, complemented
6#21443665C211yesmaximal, characteristic, complemented
7C61×#3002C211yesmaximal, characteristic
8#16839840—21no—
9#16839834—21no—
10#16839834—21no—
11D4×#92418—21no—
12#16839823—21no—
13C2×#14519704—21no—
14C2×#14519704—21no—
15#16839729—21no—
16#16839726C2211yescharacteristic
17C2×C22⋊#92418—21no—
18C2×C22⋊#92418—21no—
19C2×C22⋊#92418C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21C4×C22⋊Dic61C2211yescharacteristic
22#16839499—21no—
23#16839496—21no—
24C22×#41×C61C2211yescharacteristic
25C2×#135×C61—21no—
26C61×#525C2211yescharacteristic
27C61×#452—21no—
28C61×#451C411yescharacteristic, complemented
29C61×#450C411yescharacteristic, complemented
30C61×#449—21no—
31C61×#448C411yescharacteristic, complemented
32C61×#447C411yescharacteristic, complemented
33C61×#416—21no—
34C2×C22⋊C8×C61C2211yescharacteristic
35C2×#11758194—21no—
36C2×#11758194D411yescharacteristic
37C2×#11758194D411yescharacteristic
38C22×#92418—21no—
39C22×#92418—21no—
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C4×Dic61—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46#14519704—42no—
47#14519704—42no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418—42no—
57C22⋊#92418—42no—
58#14519688—21no—
59C4×#92418—21no—
60#14519684—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—21no—
64C2×#41×C61—21no—
65C2×#41×C61—42no—
66C2×#41×C61—42no—
67C2×#41×C61D411yescharacteristic
68C22×Q8×C61C2×C411yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61C2×C411yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61C2311yescharacteristic
73#135×C61—42no—
74#135×C61—42no—
75C2×Q16×C61—21no—
76C2×SD16×C61—21no—
77C2×SD16×C61—21no—
78C2×D8×C61—21no—
79C22×C8×C61—21no—
80#123×C61—21no—
81C22⋊Q8×C61C2×C411yescharacteristic
82C22⋊Q8×C61D411yescharacteristic
83#121×C61C2×C411yescharacteristic
84#121×C61D411yescharacteristic
85#120×C61—21no—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88#117×C61D411yescharacteristic
89#103×C61—21no—
90#103×C61—21no—
91#102×C61—21no—
92#102×C61—21no—
93C22⋊C8×C61—21no—
94C22⋊C8×C61C2×C411yescharacteristic
95C22⋊C8×C61C2×C411yescharacteristic
96C24×C61—21no—
97C24×C61#4111yescharacteristic
98#41×C61—22no—
99#41×C61—22no—
100#41×C61—22no—
101#41×C61—22no—
102#41×C61—41no—
103#41×C61—41no—
104#41×C61—41no—
105#41×C61—41no—
106#41×C61—41no—
107#41×C61—41no—
108#41×C61—42no—
109#41×C61—42no—
110#41×C61—42no—
111#41×C61—42no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—42no—
115C2×Q8×C61C22⋊C411yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—42no—
122C2×D4×C61—42no—
123C2×D4×C61—42no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C2×D4×C61C22⋊C411yescharacteristic
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×Dic61—41no—
144Q16×C61—42no—
145SD16×C61—42no—
146SD16×C61—42no—
147D8×C61—42no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—41no—
151C2×C8×C61—41no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C22⋊C411yescharacteristic
155C4⋊C4×C61C22⋊C411yescharacteristic
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—21no—
161C42×C61—21no—
162C22⋊Dic61—22no—
163C22⋊Dic61—41no—
164C4×Dic61—41no—
165C4×Dic61—41no—
166#11758194—41no—
167#11758194—41no—
168#11758194—81no—
169C2×#92418—21no—
170C2×#92418—21no—
171C2×#92418—21no—
172C2×#92418—21no—
173C2×#92418—41no—
174C2×#92418—41no—
175C2×#92418—41no—
176C2×#92418—41no—
177C2×#92418—41no—
178C2×#92418—81no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—22no—
182C23×C61—21no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—41no—
191C23×C61C4×D411yescharacteristic
192C23×C61#12111yescharacteristic
193C23×C61#12311yescharacteristic
194Q8×C61—22no—
195Q8×C61—22no—
196Q8×C61—41no—
197Q8×C61—41no—
198Q8×C61—41no—
199D4×C61—22no—
200D4×C61—22no—
201D4×C61—41no—
202D4×C61—41no—
203D4×C61—41no—
204D4×C61—42no—
205D4×C61—42no—
206D4×C61—42no—
207D4×C61—42no—
208D4×C61—41no—
209D4×C61—41no—
210D4×C61—81no—
211D4×C61—81no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×Dic61—42no—
238C2×Dic61—81no—
239C2×Dic61—81no—
240C8×C61—41no—
241C8×C61—41no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#92418—81no—
247#9037—611nomaximal, Sylow
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—42no—
261C22×C61—41no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61#38611yescharacteristic
269C22×C61#44311yescharacteristic
270C22×C61#44411yescharacteristic
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—42no—
277C4×C61—41no—
278C4×C61B(4,𝔽2)11yescharacteristic
279C4×C61B(4,𝔽2)11yescharacteristic
280Dic61—82no—
281#3002D6111yescharacteristic
282#2976—611no—
283#1789—611no—
284#1780—611no—
285#1501—611no—
286#1298—611no—
287#1282—611no—
288C2×C61—21no—
289C2×C61—21no—
290C2×C61—41no—
291C2×C61—41no—
292C2×C61—81no—
293C2×C61—82no—
294C2×C61#187611yescharacteristic
295C2×C61#188111yescharacteristic
296C2×C61#188911yescharacteristic
297C22×#41C2×D6111yescharacteristic
298C2×#135—21no—
299#525C2×D6111yescharacteristic
300#452—21no—
301#451Dic6111yescharacteristic, complemented
302#450Dic6111yescharacteristic, complemented
303#449—21no—
304#448Dic6111yescharacteristic, complemented
305#447Dic6111yescharacteristic, complemented
306#436—1221no—
307#435—1221no—
308#435—1221no—
309C8×D4—1221no—
310#433—1221no—
311C2×#104—1221no—
312C2×#104—1221no—
313#416—21no—
314#408—1221no—
315#407—611no—
316C2×C22⋊C8—611no—
317C2×C22⋊C8—611no—
318C2×C22⋊C8—1221no—
319C2×C22⋊C8—1221no—
320C2×C22⋊C8C2×D6111yescharacteristic
321C4×C22⋊C4—611no—
322#328—1221no—
323#327—1221no—
324C61#903711yescharacteristic, complemented, Sylow
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—42no—
330C2×#41—42no—
331C2×#41C22⋊D6111yescharacteristic
332C22×Q8C2×Dic6111yescharacteristic
333C22×D4—21no—
334C22×D4C2×Dic6111yescharacteristic
335C23×C4—21no—
336C23×C4C22×D6111yescharacteristic
337#135—42no—
338#135—42no—
339C2×Q16—21no—
340C2×SD16—21no—
341C2×SD16—21no—
342C2×D8—21no—
343C2×M16—611no—
344C2×M16—611no—
345C2×M16—1221no—
346C22×C8—21no—
347C22×C8—611no—
348C22×C8—611no—
349C22×C8—1221no—
350C22×C8—1221no—
351#123—21no—
352C22⋊Q8C2×Dic6111yescharacteristic
353C22⋊Q8C22⋊D6111yescharacteristic
354#121C2×Dic6111yescharacteristic
355#121C22⋊D6111yescharacteristic
356#120—21no—
357C4×D4—21no—
358C4×D4—21no—
359#117C22⋊D6111yescharacteristic
360C2×C22⋊C4—1221no—
361C2×C42—1221no—
362C4⋊C8—1221no—
363C4⋊C8—1221no—
364#104—2442no—
365#104—2442no—
366#103—21no—
367#103—21no—
368#102—21no—
369#102—21no—
370C22⋊C8—21no—
371C22⋊C8—1221no—
372C22⋊C8—1221no—
373C22⋊C8—1221no—
374C22⋊C8—1221no—
375C22⋊C8—1221no—
376C22⋊C8—1221no—
377C22⋊C8—1221no—
378C22⋊C8—1221no—
379C22⋊C8—2442no—
380C22⋊C8—2442no—
381C22⋊C8C2×Dic6111yescharacteristic
382C22⋊C8C2×Dic6111yescharacteristic
383#97—1221no—
384C4×C8—1221no—
385#95—1221no—
386C24—21no—
387C24#1175822411yescharacteristic
388#41—22no—
389#41—22no—
390#41—22no—
391#41—22no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—42no—
405C2×Q8C22⋊Dic6111yescharacteristic
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4C22⋊Dic6111yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—2441no—
428C22×C4D4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430C22×C4#1175822411yescharacteristic
431C22×C4C22×Dic6111yescharacteristic
432C22×C4C2×C22⋊D6111yescharacteristic
433C22×C4C2×C22⋊D6111yescharacteristic
434Q16—42no—
435SD16—42no—
436SD16—42no—
437D8—42no—
438M16—4881no—
439M16—2441no—
440M16—2441no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—4881no—
450C2×C8—2441no—
451C2×C8—2441no—
452C2×C8—2441no—
453C2×C8—2441no—
454C2×C8—2441no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4C22⋊Dic6111yescharacteristic
458C4⋊C4C22⋊Dic6111yescharacteristic
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—1222no—
465C22⋊C4—2441no—
466C42—21no—
467C42—2441no—
468C42—2441no—
469C23—21no—
470C23—21no—
471C23—22no—
472C23—21no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23D4×Dic6111yescharacteristic
482C23#1451974911yescharacteristic
483C23#1451975811yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—41no—
499D4—41no—
500D4—81no—
501D4—81no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—4881no—
524C2×C4—4881no—
525C2×C4—2442no—
526C2×C4C2×C22⋊Dic6111yescharacteristic
527C2×C4D4×Dic6111yescharacteristic
528C2×C4#1451974511yescharacteristic
529C2×C4#1451974911yescharacteristic
530C8—41no—
531C8—41no—
532C8—4881no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—42no—
546C22—42no—
547C22—41no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#1683964211yescharacteristic
558C22#1683987911yescharacteristic
559C22#1683988411yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—4882no—
568C4#1683994811yescharacteristic
569C4#1683994811yescharacteristic
570C2—21no—
571C2—21no—
572C2—41no—
573C2—41no—
574C2—82no—
575C2—81no—
576C2#2144614811yescharacteristic
577C2#2144618311yescharacteristic
578C2#2144622811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#3002C2
socleC22×C61#386
cosocleC23×C4×C61C23
hypercenter#3002D61
hypocenterC61#9037
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21454867C2semidirect
2. #21445763C2semidirect
3. #21445731C2semidirect
4. #21444310C2semidirect
5. #21443707C2semidirect
6. #21443665C2semidirect
28. C61×#451C4semidirect
29. C61×#450C4semidirect
31. C61×#448C4semidirect
32. C61×#447C4semidirect
301. #451Dic61semidirect
302. #450Dic61semidirect
304. #448Dic61semidirect
305. #447Dic61semidirect
324. C61#9037semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214548672
#214457632
#214457312
#214443102
#214437072
#214436652
C61×#30022
#903761